This $170,814 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (MPS) program supports collaborative research by Drexel University on the emerging applications of self-similarity in dynamical networks. The research aims to bridge analytical theories of fractals and differential equations on fractals with network science. This includes developing new tools for analyzing, predicting, and controlling self-similar network dynamics. The project will consider the Kuramoto model of coupled phase oscillators on fractal graphs, study synchronization and bifurcations in self-similar networks, and explore epidemiological networks based on an SIR model on fractal graphs. The research will contribute to advancing the scientific understanding of complex real-world networks and train graduate and undergraduate students. The project period runs from August 15, 2024 to July 31, 2027.
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